perigynium

from The Century Dictionary.

• noun In botany, the hypogynous bristles, scales, or a more or less inflated sac, which surround the pistil in many Cyperaceæ.

from the GNU version of the Collaborative International Dictionary of English.

• noun (Bot.) Some unusual appendage about the pistil, as the bottle-shaped body in the sedges, and the bristles or scales in some other genera of the Sedge family, or Cyperaceæ.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• noun botany Any unusual appendage around the pistil, such as the bottle-shaped body in the sedges, or the bristles and scales in some other genera of the sedge family.